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Popular Calculus >

y^{''}-18y=tan(x)

Solution

y^{^{''}} - 18 y = tan (x)

Solution

y = c_{1} e^{32 x} + c_{2} e^{- 32 x} + e^{32 x} \cdot \int \frac{2 e ^{- 32 x} tan ( x )}{12} d x + e^{- 32 x} \cdot \int - \frac{2 e ^{32 x} tan ( x )}{12} d x

Solution steps

y^{''} (x) - 18 y = tan (x)

Solve linear ODE:

y = c_{1} e^{32 x} + c_{2} e^{- 32 x} + e^{32 x} \cdot \int \frac{2 e ^{- 32 x} tan ( x )}{12} d x + e^{- 32 x} \cdot \int - \frac{2 e ^{32 x} tan ( x )}{12} d x

y = c_{1} e^{32 x} + c_{2} e^{- 32 x} + e^{32 x} \cdot \int \frac{2 e ^{- 32 x} tan ( x )}{12} d x + e^{- 32 x} \cdot \int - \frac{2 e ^{32 x} tan ( x )}{12} d x

Popular Examples

y^{''}+y=1,6cos(t)y(0)=0,y^'(0)=0

y^{''}-y=15t,y(0)=-15t

2(d^2y)/(dx^2)+4y^'+2y= 1/(e^x(x+1))

y^{''}+4y^'+4y=15x+17

y^{''}+16y^'+64y=100e^{2x}

Frequently Asked Questions (FAQ)

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